Study of Correlations Between Microwave Transmissions and Atmosph

8/10/2019 Study of Correlations Between Microwave Transmissions and Atmosph

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Te Florida State University DigiNole Commons

Electronic eses, Treatises and Dissertations e Graduate School

11-30-2010

Study Of Correlations Between MicrowaveTransmissions And Atmospheric E ects Andrew James StringerFlorida State University

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Recommended CitationStringer, Andrew James, "Study Of Correlations Between Microwave Transmissions And Atmospheric E ects" (2010). Electroniceses, Treatises and Dissertations.Paper 396.
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T HE FLORIDA STATE UNIVERSITY

C OLLEGE OF ENGINEERING

STUDY OF C ORRELATIONS BETWEEN M ICROWAVE TRANSMISSIONS AND

ATMOSPHERIC EFFECTS

By

ANDREW J. STRINGER

A Thesis submitted to theDepartment of Electrical and Computer Engineering

in partial fulfillment of therequirements for the degree of

Master of Science

Degree Awarded:Fall Semester, 2010


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The members of the Committee approve the thesis of Andrew J. Stringer defended on November30 th, 2010.

Dr. Simon Y. FooProfessor Directing Thesis

Dr. Ming YuCommittee Member

Dr. Bruce A. HarveyCommittee Member

Approved:

Dr. Simon Y. Foo, Chair, Department of Electrical and Computer Engineering

Dr. Ching-Jen Chen, Dean, College of Engineering.

The Graduate School has verified and approved the above-named committee members.


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ACKNOWLEDGEMENTS

I would like to thank and express my deepest appreciation to Dr. Simon Y. Foo and thank himfor his constant encouragement, criticism, perspectives, and ongoing inspiration. As a thesis

director, teacher, and friend to me, you have been an invaluable resource and have helped me

tremendously to complete this thesis.

I would like to thank Dr. Bruce A. Harvey as a valued committee member and for your guidance

and knowledge in rain attenuation models and wireless communications.

I also want to thank committee member Dr. Ming Yu for helping me challenge myself and enrich

my knowledge in computer programming.

I would like to extend a special thank you to William R. Allen, P.E. for his extended support,

criticism, and knowledge in wireless communications through the course of this project.

I would like to thank members of Florida Department of Transportation Traffic Engineering

Research Lab, specifically Ron Meyer, Vernell Johnson, and Derrick Vollmer, for their ongoing

efforts in helping make this project a success.

I would also like to thank Florida Department of Transportation District Three employee, Mark

Nallick for his programming knowledge and support.

I would also like to thank the Florida State University - College of Engineering Department of

Electrical and Computer Engineering, RCC Consultants, Inc., the Florida Department of

Transportation, and the RWIS and Clarus Initiative projects for their ongoing grants, assistance,

and support that made this research possible.

Finally, I would like to express my love for my parents, Michael and Barbara, my brothers, Nick

and Chris, and my partner, Christina Katopodis for their unfaltering support and encouragement,

and always believing in me. I could not have finished this manuscript without you. I love you

all.


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iv

T ABLE OF C ONTENTS

LIST OF TABLES ........................................................................................................................ viLIST OF FIGURES ..................................................................................................................... vii

LIST OF ABBREVIATIONS .......................................................... ............................................. ix

ABSTRACT .................................................................................................................................. xi

1. I NTRODUCTION ...................................................... ........................................................ .......1

1.1. Overview ..................................................... ........................................................ .............1

1.2. Motivation ...................................................... ....................................................... ...........4

1.3. Problem Statement ................................................. ................................................... ........4

1.4. Scope of Work ............................................... ................................................... ................5

2. CRANE ATTENUATION MODELS ....................................................... ...............................6

2.1. Global (Crane) Model .......................................................................................................6

2.2. Initial Two-Component Model ........................................... ..............................................9

2.2.1. Volume Cell Contribution...................................................... ...................................9

2.2.2. Debris Contribution ................................................ ................................................12

2.2.3. Probability of Terrestrial Rain Rate .................................................. ......................132.2.4. Attenuation along a LOS Path ................................................. ...............................14

2.3. Revised Two-Component Model .......................................................... .........................15

2.3.1. Model for Volume Cell Contribution ..................................................... ................15

2.3.2. Model for Debris Contribution ........................................................ .......................15

3. ITU ATTENUATION MODEL AND OTHER ATTENUATION MODELS .....................16

3.1. International Telecommunications Union Model ..................................................... ......16

3.2. Other Attenuation Models ............................................... ...............................................214. COMPUTER SIMULATION R ESULTS AND K EY FINDINGS .......................................22

4.1. Data Acquisition ...................................................... .......................................................22

4.2. Crane Models, ITU Model, and Path Loss 4.0 Analysis ................................................24

4.2.1. Analysis of Data Using Crane Models ........................................................... .........24


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4.2.2. International Telecommunications Union Model Analysis ....................................25

4.2.3. Path Loss 4.0 Analysis ................................................. ...........................................26

4.2.3.1. Greenville Analysis ................................................. .....................................27

4.2.3.2. Lake City DOT Analysis ................................................. .............................29

4.2.3.3. SR-222 Analysis ...................................................... .....................................31

4.3. Correlation Analysis without Data Preprocessing ..........................................................33

4.4. Fast Fourier Transform and Power Spectrum Analysis ........................................... ......38

4.4.1. Fast Fourier Transform Analysis ........................................................... .................38

4.4.2. FFT Spectrum Analysis ............................................ ..............................................39

4.4.3. Correlation Analysis ...................................................... .........................................41

4.5. Short Time Fourier Transform and Power Spectrum Analysis ......................................41

4.5.1. Short Time Fourier Transform Analysis .................................................. ...............41 4.5.2. STFT Power Spectrum Analysis ................................................ .............................42


4.6. Discrete Wavelet Transform and Wavelet Decomposition Analysis .............................44

4.6.1. Wavelet Decomposition Analysis .......................................... .................................44


4.7. Key Findings ................................................ ........................................................ ..........52

5. CONCLUSION AND FUTURE WORK ...............................................................................565.1. Conclusion ..................................................... ........................................................ .........56

5.2. Future Work and Recommendations ..................................................... .........................57

APPENDIX A: PROGRAM CODE ........................................................ ....................................59

APPENDIX B: DEVICE SPECIFICATIONS AND DATASHEETS .......................................75

BIBLIOGRAPHY .........................................................................................................................88

BIOGRAPHICAL SKETCH ........................................................................................................90


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L IST OF T ABLES

Table 3.1: ITU Rain Rate Data for 0.001% Rain Fades in the Americas .....................................17Table 3.2: Interpolated Regression Coefficients for 1-30 GHz ....................................................20

Table 3.3: ITU Rainfall Rates for Different Probabilities and Rain Regions ........................... ..21

Table 4.1: Path Loss 4.0 Print Summary for Greenville ................................................ ...............28

Table 4.2: Path Loss 4.0 Print Summary for Lake City DOT .......................................................30

Table 4.3: Path Loss 4.0 Print Summary for SR-222 ...................................................................32

Table 4.4: Correlation Coefficients for Greenville .................................................. .....................33

Table 4.5: Correlation Coefficients for Lake City DOT ....................................................... ........33

Table 4.6: Correlation Coefficients for SR-222 ........................................................ ....................34

Table 4.7: RSL Correlation Coefficients of the Chosen Sites ................................................. .....34

Table 4.8: RSL and Weather Parameter Cross-Correlation Coefficients for

Greenville .................................................... ........................................................ .........35


Lake City DOT ............................................................................................................36


SR-222 ......................................................................................................................37Table 4.11: FFT Correlation Coefficients for Greenville .................................................... .........41

Table 4.12: Correlation Coefficients of Three Level Wavelet Decomposition for

Greenville ................................................. ........................................................ .........51


Lake City DOT .........................................................................................................51


SR-222 ......................................................................................................................52


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L IST OF F IGURES

Figure 1.1: A Typical Communication System ................................................... ...........................1Figure 1.2: FDOT Statewide Telecommunications Network Deployment Map ............................3

Figure 2.1: Multiplier in the Power-Law Relationship between Specific

Attenuation and Rain Rate ...........................................................................................7

Figure 2.2: Exponent in the Power-Law Relationship between Specific

Attenuation and Rain Rate ...........................................................................................8

Figure 2.3: Edfs for the Joint Occurrence of Reflectivity and Square Root Area .......................10

Figure 2.4: Average Area of Volume Cells as Measured and Modeled Using an

Exponential Square Root Area Model ....................................................... .................11

Figure 3.1: ITU Atmospheric Attenuation Prediction ..................................................................17

Figure 3.2: ITU Rain Regions for the Americas .................................................. .........................18

Figure 3.3: ITU Rain Regions for Europe and Africa ..................................................................19

Figure 3.4: ITU Rain Regions for Asia ........................................................ .................................19

Figure 4.1: Sample Comma-Delimited Text File from the Control Module at

Greenville ESS site ................................................ .....................................................23

Figure 4.2: Weather Master 2000 TM Example ..............................................................................23Figure 4.3: Netboss Example .................................................... ....................................................24

Figure 4.4: ITU Model Rain Attenuation Prediction for Greenville Site .....................................25

Figure 4.5: ITU Model Rain Attenuation Prediction for Lake City DOT Site .............................26

Figure 4.6: Path Loss 4.0 Path Profile for Greenville .................................................. .................27

Figure 4.7: Path Loss 4.0 Path Profile for Lake City DOT ...........................................................29

Figure 4.8: Path Loss 4.0 Path Profile for SR-222 .......................................................................31

Figure 4.9: FFT of Greenville RSL and ESS data ........................................................ ................38

Figure 4.10: Enlarged Window of the FFT of Greenville RSL and ESS data ..............................39

Figure 4.11: Power Spectrum of Greenville RSL and ESS Data for One Day .............................40

Figure 4.12: Power Spectrum of Greenville RSL and ESS Data for a One Hour ........................40


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Figure 4.13: RSL STFT at 45 Angle for Greenville ESS Rotated Approximately 180 ............42

Figure 4.14: RSL STFT Power Frequency vs. Amplitude for Greenville ESS ............................43

Figure 4.15: RSL STFT Power Time vs. Amplitude for Greenville ESS.....................................43

Figure 4.16: Discrete wavelet transform illustration .................................................. ..................45

Figure 4.17: Stages of a Three Level Wavelet Decomposition ............................................... .....46

Figure 4.18: Wavelet Decomposition of Precipitation and RSL for Greenville Data ..................47

Figure 4.19: Wavelet Decomposition for RSL, RH, and T at Greenville ESS Site .....................48

Figure 4.20: Enlarged Wavelet Decomposition for Greenville Data ............................................48

Figure 4.21: Wavelet Decomposition of Precipitation and RSL for Lake City DOT Data ..........49

Figure 4.22: Enlarged Wavelet Decomposition for Lake City DOT data ....................................49

Figure 4.23: Wavelet Decomposition of Precipitation and RSL for SR-222 data ........................50

Figure 4.24: Enlarged Wavelet Decomposition for SR-222 data ......................................... ........50Figure 4.25: Greenville Data during First Week of April, 2010 ............................................ .......53

Figure 4.26: Three Level Wavelet Decomposition for Greenville Data ...................................... .54

Figure 4.27: Enlarged Three Level Wavelet Decomposition for Greenville Data .......................54


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L IST OF ABBREVIATIONS

F Degrees FahrenheitBP Barometric Pressure

BS Base Station

CCIR International Radio Consultative Committee

CWS Columbia Weather Systems

dB Decibel

DP Dew Point

DFT Discrete Fourier Transform

DWT Discrete Wavelet Transform

GUI Graphical User Interface

EDF Empirical Distribution Function

EM Electromagnetic

ESS Environmental Sensor Station

FDOT Florida Department of Transportation

FFT Fast Fourier Transform

GHz GigahertzHI Heat Index

IEEE Institute of Electrical and Electronics Engineers

ITS Intelligent Transportation System

ITU International Telecommunications Union

ITU-R International Telecommunications Union Radio Communications

LOS Line of Sight

QC Quality Control

P Precipitation

RF Radio Frequency

RH Relative Humidity

RSL Received Signal Level

RWIS Road Weather Information System


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RX Receiver

SR-222 Gainesville Research Site

STFT Short Time Fourier Transform

STN Statewide Telecommunications Network

T Temperature

TX Transmitter

USDOT United States Department of Transportation

WC Wind Chill

WD Wind Direction

WS Wind Speed

WSA Wind Speed Average


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ABSTRACT

Understanding the effects of atmospheric conditions with respect to microwave propagation and performance is critical to the design and placement of microwave antennas for modern

communication systems. Weather data acquisition in the state of Florida is underdeveloped and

the published effects of weather on microwave communications are limited to general models

based on large regional climate models. The goal of this research is to correlate atmospheric

conditions and microwave transmission via the existing Florida Department of Transportation

(FDOT) Road Weather Information System (RWIS) network, new Environmental Sensor Station

(ESS) sites, and Harris Corporation network management software Netboss. The microwave

radios in the FDOT microwave infrastructure through powerful Netboss scripting tools and

options are utilized to record the received signal level (RSL) output of the microwave radios for

signal analysis. This RSL data is analyzed and correlated with the acquired ESS weather data to

determine basic atmospheric effects on microwave propagation.

Methods for analysis of correlated data include existing atmospheric attenuation

models, such as the Global (Crane) and International Telecommunications Union (ITU) models,

and empirical methods such as the Fast Fourier Transform (FFT), Short Time Fourier Transform

(STFT), Discrete Wavelet Transform (DWT) and wavelet decomposition, and correlationanalysis of each method used. The data is treated as a discrete non-stationary signal. Results do

not show a clear correlation between receiver signal level (RSL) and weather parameters for

several of the test methods. Testing the correlation and cross correlation of the raw data yielded

weak correlation. The simulation of rain attenuation via the ITU model displayed weak

insignificant results for the sets of RSL data. The FFT and STFT both incorporate too much

noise and distortion to accurately compute a correlation.

Wavelet decomposition shows a strong correlation between several weather

parameters and a weak correlation for others. This result confirms the wavelet decomposition

analysis and agrees with trends found in the RSL and weather parameters. Further analysis

points to multipath fading and atmospheric ducting. During early hours of the morning,

reflections from moist surfaces, such as tree foliage and other terrestrial objects, water vapor and

dew will cause transmitted signals to reach the receive antenna out of phase, which will cause


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attenuation or gain while atmospheric ducting will cause gain in the RSL and is visible in the

acquired data. It is concluded that weather conditions such as water vapor, mist, and rising fog

have an effect on microwave propagation.


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paths of the microwave system are experiencing more outages than the design anticipated. The

goal of this proposed project is to add new Environmental Sensor Stations (ESS) to the existing

FDOT Road Weather Information System (RWIS) and correlate the acquired weather data to

collected Received Signal Level (RSL) data to build a better understanding of atmospheric

effects on microwave transmission in the state of Florida at approximately 6.8 GHz. This

manuscript will provide a significant outlook on current attenuation modeling in the northern

region of the state of Florida due to environmental and atmospheric effects.

This project incorporates existing RWIS ESS sites via the FDOT Engineering and

Operations Office, Intelligent Transportation Systems (ITS) section, located in Tallahassee.

Columbia Weather Systems (CWS) Capricorn 2000 TM data loggers and Weather Master 2000 TM

software are used to collect and log atmospheric data, respectively. Three RWIS ESS sites and

six microwave sites will be utilized to gather crucial weather and microwave RSL data foranalysis. The FDOT microwave tower sites chosen for analysis are Greenville, Lake City DOT,

and Gainesville (interchange of SR-222 and I-75). See Figure 1.2 for chosen ESS sites in the

FDOT statewide microwave infrastructure deployment map.

The microwave RSL data is obtained via Netboss; a proprietary network management

software program developed by Harris Corporation that interfaces with the SCAN channel of the

FDOTs Harris DVM-6 Excel microwave radios in the FDOT microwave infrastructure. In

addition to many imbedded monitoring and maintenance features, Netboss also has powerful

scripting abilities and tools via a UNIX based VI editor. New scripts will be written in Netboss

to utilize the state of Floridas existing RWIS ESS sites to gather microwave RSL data for

analysis. Methods and models for the analysis of acquired data include Global (Crane) model,

Initial and Revised Two-Component model, International Telecommunications Union (ITU) rain

region model, and Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT),

Discrete Wavelet Transform (DWT), and wavelet decomposition. The project work is conducted

with RCC Consultants, Inc. and the FDOT for access to the FDOT microwave communication

infrastructure, shelter sites, and the Traffic Engineering Research Lab (TERL) weather data

server and data loggers.


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Figure 1.2: FDOT Statewide Telecommunications Network Deployment Map

This project involves a number of different sensor types, mountings, locations across the

state of Florida, data interpretation and correlation, considered analysis methods, and includes

many communication protocols for data acquisition and performance comparison purposes. In

addition to better understanding microwave transmission attenuation and performance, an added

benefit of the proposed project is that it also provides invaluable weather data to the United

States Department of Transportation (USDOT) Clarus initiative; a national weather data

acquisition initiative.


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1.2. Motivation

Many research efforts have been devoted to modeling path loss propagation attenuation due to

atmospheric effects, specifically rain, water vapor, and fog, on microwave links by using

different methods ranging from analytical models and semi-empirical models, to observation

measurements. Most radio signal propagation models are developed using empirical methods,

based on fitting mathematical models to measured data. In recent years, few measurement-based

point rain rate attenuation models have been proposed and investigated. Leading models for path

loss attenuation due to atmospheric effects have been proposed by Robert K. Crane and the ITU

[1]-[5] and are in use in several path loss analysis programs by renowned RF manufacturers,

consulting firms, and engineering practices. These research works were primarily focused on

particular regions and a general model was developed and deployed for areas that do not produce

significant data.Given the numerous weather conditions, and the lack of real-world observation modeling

in the state of Florida, it is desirable to correlate observations of Floridas atmospheric conditions

to the RSL of FDOTs statewide telecommunications network to better understand the impact

weather has on microwave transmission.

1.3. Problem Statement

There are many techniques and methods used to develop attenuation models which are later used

in path loss models. The Global (Crane) model and the ITU model are the most commonly used

models to calculate attenuation due to major atmospheric effects; mainly rain with some

discussions regarding water vapor and fog modeling on a terrestrial path link. Traditional

techniques for estimating losses due to atmospheric effects focus on the dominant source of

fading - rain attenuation. The focus of this project is the study of several atmospheric attributes

and their effect on microwave received signal levels, not on rain attenuation alone. The

hypothesis of this research is that various atmospheric conditions such as relative humidity,

temperature, wind, and rain will have an impact on microwave transmission.


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1.4. Scope of Work

The organization of this manuscript is as follows: Chapter 2 presents current attenuation path

loss models, focusing specifically on Robert K. Cranes volume cell and debris attenuation

models; Chapter 3 introduces the ITU rain attenuation model and provides some other commonly

used models based on observations, frequencies, regions, and estimations. The analyzed data

using selected models and observed data along with theoretical path loss models will be provided

in Chapter 4 which also includes comparisons with the empirical models and key findings from

correlated results. Finally, Chapter 5 provides a conclusion and recommendations for future

work.


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C HAPTER 2

C RANE A TTENUATION M ODELS

Different attenuation models are studied and used as a comparison method for the acquired data.

In this chapter the Global (Crane) Model, Initial Two-Component Model, and Revised Two-

Component Model are discussed in detail. Their relationship to the goal of this manuscript will

be discussed in Chapter 4.

2.1. Global (Crane) ModelThe Global (Crane) Model was developed by Robert K. Crane (1980), a pioneer in rain

attenuation modeling, for use in Earth-space or terrestrial links. The Global model is based

entirely on geophysical observations of rain rate, rain structure, and the vertical variation of

atmospheric temperature. None of the model constants are obtained from attenuation

measurements [2]. A statistical model is required to provide an accurate estimate of attenuation

due to rain being characteristically inhomogeneous on the horizontal plane. In Cranes model

the horizontal structure of rain is not dependent on the climate region. This is due to the fact that

the fluid dynamics parameters that are used to characterize flow are weakly dependent on

climate. This model uses the multiplier coefficient ( k ) and exponent ( ) of the power-law

equation (2.1) for the approximation of spherical drops at an assumed temperature of 32 F andthe dielectric constant model for specific frequencies ranging from 1 to 1000 GHz. See Figures

2.1 and 2.2 for multiplier and exponent plots.

(2.1)The polarization state of an antenna has little effect in determining the prediction of

attenuation along a terrestrial link, either experimentally observed or calculated using the k multiplier and exponent plots.


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Figure 2.1: Multiplier in the Power-Law Relationship between Specific Attenuation and Rain

Rate. (Figure 4.3 from Ref. 2, courtesy of Wiley.)

The simplest path profile for attenuation due to rain rate is shown in equations 2.2 and

2.3. When this equation integrated it produces the observed median power law relationship,

which is the derivative of the power law relationship with respect to path length.

, 0 (2.2) , 22. (2.3)

where

horizontal path attenuation (dB)

rain rate (mm/h)

path length (km) specific attenuation, = (dB/km)and the remaining coefficients are the empirical constants of the piecewise exponential model:

ln 0.83 0.17ln 0.026 0.03 km


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3.8 0.6 km km

km

km Cranes model provides a prediction for attenuation along a terrestrial Line of Sight (LOS) linkfor the path-integrated rain rate given equiprobable value of rain rate.

Figure 2.2: Exponent in the Power-Law Relationship between Specific Attenuation and Rain

Rate. (Figure 4.4 from Ref. 2, courtesy of Wiley.)

The Global Model employs data sets for various probabilities and availabilities that differ

from the ITU model, discussed later in section 3.1, and are only valid for distances up to 22.5

km. The Global Model does not employ an availability adjustment factor like the ITU model. If

the desired availability is not represented in the Crane data, it is possible to logarithmically

interpolate the given data to estimate the rain rate [1]. This method has been tested to provide

reasonable information, but is not sanctioned by Crane.


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2.2. Initial Two-Component Model

The Two-Component Model for attenuation due to rainfall was initially based on the observation

of volume cells and debris, and an ad hoc procedure. These observations account for the spatial

correlations for each component and was eventually revised to account for vertical rainfall as

well as rainfall along a horizontal path. This model requires parameters for the two-component

rain rate distribution model and is therefore more complex if the global rain rate climate model is

not invoked, and thus the first step in the consideration of the more complex modeling problems

and the only step allowing for comparison with a significant body of measurements [2].

The Two-Component Model accounts for the contributions of heavy rain showers and

lighter intensity rain showers occurring in larger regions. RF propagation does not always

intersect a single cell or debris, or both along a LOS link; thus the model accounts for volume

cells and debris independently. The Two-Component Model assumes either a single volumecell, only debris, or both, along a LOS link. This design is in place so a desired attenuation

threshold is not exceeded. The probability for each component, a volume cell of rain or debris, is

calculated and the results are summed for the total desired probability estimate.

2.2.1. Volume Cell Contribution

In this model the path-integrated, or terrestrial, rain-rate is given by

(2.4)where observed path-integrated value (km mm/h) rain-rate profile along path (mm/h) length of path (km)The volume cell contribution for the path-integrated rain rate is approximated by

(2.5)

where

peak rain rate in volume cell average dimension of volume cell with area and rain rate, C (see figs. 2.3 and 2.4) with 1.70 and 0.002 adjustment factor required by definition of volume cell


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Figure 2.4: Average Area of Volume Cells as Measured and Modeled Using an Exponential

Square Root Area Model. Data from Kansas HIPLEX [Crane and Hardy, 1981]. (Figure 2.32from Ref. 2, courtesy of Wiley.)

Equation 2.7 is the starting point in the particular application of the model where

is given and and are to be determined. The average dimension of volume cell, , ismodeled by

(2.8)Taking min

, yields

. 0 or

1 0


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and

(2.9)

(2.10)

The initial two-component model is simplified by the assumption that all volume cells

have the same cross-sectional area. The area of influence of the volume cell about a point is ,

and the area of influence of a circular volume cell about a line of length is

1 1 (2.11)where is the average length of a line through a circular volume cell and given by

12

0.9

Crane approximates by since both the area and shape of the cell are uncertain, where

Assuming only one volume cell can occur at random anywhere along the path, affect the

LOS link at any instance of time, and the random volume cell spatial distribution is uniformly

distributed, the probability of occurrence of the rain rate value for the center of a single volume

cell is given by [2]. The probability of exceeding the specified occurrence of rainrate for the center of a single volume cell is given by 1 1 1 (2.12)

2.2.2. Debris Contribution

To effectively calculate the debris contribution on a terrestrial path link, the spatial scale has

to be associated with the rain within the debris. Crane and Hardy (1981) provided data on the

relationship between average rain rate and area for isolated echo areas. This data is used to


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create a relationship between spatial scale and the average rain rate within the debris. The

result is a regression line fit for the relationship area versus rain rate.

882. (km 2) (2.13)where is the debris area

29.7. (km) (2.14) 1 The physical path length D or the debris scale length , whichever results is the

smallest, is used in the calculation for a specified path integrated rain rate. For a long path,

. . Thus,

. . and 29.7. 170. (km 2) (2.15)

For a path of length D, min ,

(2.16)

29.7

. (2.17) 1 (2.18)2.2.3. Probability of Terrestrial Rain Rate

The Two-Component Model scaling parameters and are assumed to apply in all climate

regions due to the similarity in scale of the dynamic processes responsible for precipitation. The

probability for path integrated rain rate I is

(2.19)The model cannot be used directly if the interest of probability is known and the value of I isestimated. The values of probability must be calculated for a number of trial I values [2] then

interpolate or iteratively adjust the trial value of I until the interest of probability is estimated.


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2.2.4. Attenuation Along a LOS Path

The attenuation along a LOS path is given by (2.20) and attenuation within a volume cell is

approximated by (2.21).

(2.20)

(2.21)The adjustment factor to estimate additional attenuation outside a volume cell is

0.7 (2.22)For a Gaussian volume cell profile, the errors in calculating attenuation caused by

assuming the verses relationship in equation 2.22 are 3.5% for 1.3 and 4.5% for 0.75 [2]. Thus for frequencies between 1 GHz and 100 GHz the error is less than 5% forentire range of (assuming Gaussian cells).

The two-component model estimates the rain rate in a volume cell and debris region and

calculates the probability of exceeding a certain threshold or attenuation value.

For a volume cell,

. (2.23) min , (2.24)

(2.25)

(2.26) 1 (2.27) Neglecting the effect of the nonlinearity on the relationship between specific attenuation and the

average rain rate within a debris region yields

. . (mm/h) (2.28) 29.7. (2.29)Then, min , (2.30)

(2.31) 29.7 . (2.32)


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1 (2.33)The probability that the attenuation value a is exceeded is given by

(2.34)

2.3. Revised Two Component Model

The Revised Two-Component Model (R. K. Crane and H. C. Shieh; 1989) is an extension and

refinement of the initial model by Robert K. Crane. The refinements include a more realistic

treatment of the statistical variations and spatial correlations of rain within the cell and debris

components of the initial model [2]. The revised model has similar derivations as the initial two-

component model, hence all intermediate steps and equations for the volume cell and debris

components will be omitted with the exception of the final attenuation and probability equations.

2.3.1. Model for Volume Cell Component

Rain cells often cause severe attenuation to transmitted signals over short time intervals. The

Revised Two-Component Model assumes constant specific attenuation with height and only

considers reduced attenuation on horizontal path links. The model also assumes that a spatial

rain rate profile along a horizontal line through a rain cell has a Gaussian distribution and the

occurrence for probability density for a rain cell is uniform. Thus, the attenuation is

2 (2.35)and the probability of exceeding a specific attenuation is define as

A ,, (2.36)2.3.2. Model for Debris Component

The probability density function for the debris component of the mixed rain rate process is

assumed to be jointly lognormal with the spatial correlation function for the variations in thelogarithm of the rain rate derived from radar observations [2].

ln (2.37)The final probability of exceeding a specified attenuation is the sum of and .


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C HAPTER 3

ITU A TTENUATION M ODEL

Different attenuation models were studied and used in a comparison method for the acquired

data. This chapter discusses, the International Telecommunications Union Model in detail along

with other attenuation models. The relationship of the ITU Model to the goal of this manuscript

will be discussed in chapter 4.

3.1. International Telecommunications Union Model Nearly 100 years after the ITU was formed in 1865, several ITU members began focusing on

research and development of rain attenuation models and the effects the environment and

atmosphere have on RF propagation links. Similar to Cranes work, the ITU developed a global

rain model that incorporates rain region factors based on acquired meteorological data. The ITU

Model for a given availability on a horizontal or nearly horizontal communications link is to

determine the 99.999% fade depth [1]. Different fade depths are available and shown in Table

3.3. The five-nines data has lower confidence than four-nines data due to a smaller database,

however, the five-nines data will be viewed for this project, as five-nines is the industry standard

for public safety in Florida for LOS link reliability.

Atten 0.001 (dB) (3.1)where

is the 99.999% rain rate for the rain region, in mm/h

is the specific attenuation in dB/km is the link distance in km

and the distance factor r 1/1 /0 (3.2)with the effective path length

0 35. (km) (3.3)


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The specific attenuation is calculated by using the defined 99.99% rain rate region of the

corresponding region of interest. The ITU rain rate data for 0.001%, or five-nines, rain fades in

the Americas is shown in Table 3.1. The regression coefficients, and , for frequencies 1-30

GHz and horizontal polarization are listed in Table 3.2. Rain rates based on geographical

regions are the most widely used and easily applied method for determining the rain rate [1].

Table 3.1: ITU rain rate data for 0.001% rain fades in the Americas

A B C D E F G H J K L M N P22 32 42 42 70 78 65 83 55 100 150 120 180 250

Source : Table 1 from Ref. 5, courtesy of the ITU.

Figure 3.1 shows specific attenuation of frequencies ranging from 1 GHz to 100 GHz due to

water vapor, dry air, and the sum of water vapor and dry air. Major specific attenuation is

apparent at 22.5 GHz and 60 GHz frequencies.

Figure 3.1: ITU Atmospheric Attenuation Prediction


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The ITU model factors to model rain attenuation are not linear with distance, thus simply

multiplying the specific attenuation with distance will not calculate the correct estimate of the

attenuation over the LOS link. The ITU model is validated for frequencies up to at least 40 GHz

and distances up to 60 km [6]. The desired probability

100Availa expressed as a

percentage for latitudes greater than 30 degrees, North or South,

Atten/Atten 0.001 0.12 0.546 0.0 (3.4)and less than 30 degrees, North or South,

Atten/Atten 0.001 0.07 0.855 0.1 (3.5)ITU rain regions for the Americas, Europe and Africa, and Asia are shown in Figure 3.2, 3.3, and

3.4, respectively.

Figure 3.2: ITU Rain Regions for the Americas. (Figure 1 from Ref. 5, courtesy of the ITU.)


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Figure 3.3: ITU Rain Regions for Europe and Africa. (Figure 2 from Ref. 5, courtesy of ITU.)

Figure 3.4: ITU Rain Regions for Asia. (Figure 3 from Ref. 5, courtesy of the ITU.)


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Table 3.2: Interpolated Regression Coefficients for 1-30 GHzf(GHz) H H V V 1 3.87 10 0.912 3.52 10 0.88 2 1.54 10 0.963 1.38 10 0.9233

3.576 10

1.055

3.232 10

1.012

4 6.5 10 1.121 5.91 10 1.0755 1.121 10 1.224 1.005 10 1.18 6 1.75 10 1.308 1.55 10 1.2657 3.01 10 1.332 2.65 10 1.312 8 4.54 10 1.327 3.95 10 1.319 6.924 10 1.3 6.054 10 1.286 10 0.01 1.276 8.87E-3 1.26411 0.014 1.245 0.012 1.231 120.019

1.217 0.017 13 0.024 1.194 0.022 1.174 14 0.03 1.173 0.027 15 0.037 1.154 0.034 1.128 16 0.043 1.142 0.039 17 0.05 1.13 0.046 1.101 18 0.058 1.119 0.053 19 0.066 1.109 0.061 1.076 20 0.075 1.099 0.069 21 0.084 1.091 0.077 1.057220.093

1.083 0.085 23 0.103 1.075 0.094 1.043 24 0.113 1.068 0.103 1.03625 0.124 1.061 0.113 1.03 26 0.135 1.052 0.123 27 0.147 1.044 0.133 1.017 28 0.16 1.036 0.144 29 0.173 1.028 0.155 1.006 30 0.187 1.021 0.167 Source : Table 10A.2 from Ref. 1, courtesy of John S. Seybold.


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Table 3.3: ITU Rainfall Rates for Different Probabilities and Rain RegionsPercentageof Time (%) A B C D E F G H1.0


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C HAPTER 4

C OMPUTER SIMULATION R ESULTS AND K EY F INDINGS

A variety of software is used to compile and process all acquired data. This chapter describes

software utilized in this project, specifically Weather Master 2000 TM, MATLAB R2007b,

Netboss, and Microsoft Excel, and incorporates discussions of various methods of analysis. This

chapter also displays tables and figures with explanations, arguments, and supporting evidence

for each method used.

4.1. Data Acquisition

An array of software is utilized to acquire data from each site and store it in a format that can be

further processed. The Capricorn 2000 TM weather station control module is a programmable

microprocessor with abundant on-board memory. The Capricorn 2000 Weather Display can

display weather information, perform complex computations, and store relatively large amounts

of weather data [10]. It incorporates a built-in circular data logger which can hold up to 511

records of sensor readings (samples) and High/Low information. The data logger can output

stored data in a comma-delimited text file as shown in Figure 4.1.

The Capricorn 2000 TM control module at each site communicates with a proprietary

software, Weather Master 2000 TM, on the FDOT ESS server located at the TERL in Tallahassee,

FL. The Weather Master 2000 TM software has a graphical user interface (GUI) and incorporates

many weather statistics as shown in Figure 4.2, but the software was not reliable due to data

recording failures. This inconsistency created holes in the acquired data records and posed a

major problem for this project. The software bug was fixed after a series of updates and patches

provided by the manufacturer, and the missing data was filled by interpolation. This did notsolve the issue completely as some holes in the data were so large that interpolation could not

accurately convey the missing data. In this case data from external sources is used. Archived

weather data from www.weather.com and www.wunderground.com are used to assist in filling

some of the larger sections of missing data. Many MATLAB scripts were written to scan the


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Figure 4.3: Netboss Example

4.2. Crane Models, ITU Model, and Path Loss 4.0 Analysis

Some models used for attenuation calculations and predictions were researched prior to data

acquisition, and are examined with the data to determine their reliability in the state of Florida.

4.2.1. Analysis of Data Using Crane Models

The Greenville and Monticello, Lake City DOT and US-41, and SR-222 and US-41 signal paths

chosen for research are 24.38 km, 22.27 km, and 37.59 km in length, respectively, and the

Global (Crane) Model, Initial Two-Component Model, and Revised Two-Component Model arevalid for distances up to 22.5 km. The most reliable site, in terms of working weather sensors, is

Greenville, and most analysis methods in this manuscript are computed using data from the

Greenville site. Due to the restriction of distance and the lack of accurate weather data, no

further analysis of data using Cranes models is computed.


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4.2.2. International Telecommunications Union Model Analysis

The Greenville and Lake City DOT site data is analyzed using the ITU model. Given the

frequency of 6.835 GHz and a horizontal antenna polarization, the calculated linear regression

coefficients, and , are 0.0028 and 1.3280, respectively. The linear regression coefficient

values are linearly interpolated using MATLAB. The program code is located in Appendix A.

The Greenville rain data is converted from inches per hour (in/h) to millimeters per hour (mm/h)

and the predicted rain attenuation is calculated for Greenville using the recorded mm/h rain rate.

The predicted rain attenuation is displayed in Figure 4.4 and Figure 4.5. The minimum and

maximum attenuation due to rain are 0 dB and 0.1549 dB, respectively. This very small amount

of attenuation has little effect on the received signal, and the RSL displays periodic attenuation

patterns that vary in amplitude much greater than the calculated rain attenuation. Research

points to other weather parameters causing the major attenuation cycles discussed in latersections in this chapter.

Figure 4.4: ITU Model Rain Attenuation Prediction for Greenville Site


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Figure 4.5: ITU Model Rain Attenuation Prediction for Lake City DOT Site

The code for the ITU model and regression coefficient interpolation can be found in Appendix A

of this manuscript.

4.2.3. Path Loss 4.0 Analysis

Path Loss 4.0 is used by the FDOT to determine the reliability of a communications link in the

Statewide Telecommunications Network (STN). The FDOT requires five-nines of reliability for

the STN. Tables 4.1 through 4.3 contain summary data from Path Loss 4.0. The reliability

method for analysis is the Vigants-Barnett method and the selected rain attenuation model is the

ITU-R P530-7. The ITU-R P530-7 is the full model name for the ITU model discussed in

Chapter 3. Figures 4.6 through 4.8 display a print profile of the sites that were analyzed. This

profile contains information regarding the antenna height, distance between sites, terrain layout,

and much more data that give engineers and designers a clear view of the current or future

site/system under analysis.


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4.2.3.1. Greenville Analysis

The Greenville site is located one mile west of Greenville, FL on the Interstate 10 westbound

route. The majority of the terrestrial path between the Greenville and Monticello DOT sites is

populated with 60 ft trees, shown in green in Figure 4.7. There are some buildings located along

the path link, but their heights are only a fraction of that of the trees and thus can be ignored.

This, however, does not interfere with the LOS link due to the antenna heights; the first Fresnel

Zone is not breached. The LOS link is displayed in red and the bottom half of the first Fresnel

Zone is displayed in blue. The Path Loss 4.0 print summary, shown in Table 4.1, contains

information about the microwave radio used in this project among other site data. The FDOT

requires five-nines of reliability for the STN and based on the given criteria Path Loss 4.0

calculated Greenvilles annual multipath plus rain (%-sec) of 99.99432 and 1791.07 in

percentage and seconds, respectively. This is below FDOT standards and has been reported toFDOT ITS engineers.

Figure 4.6: Path Loss 4.0 Path Profile for Greenville


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4.2.3.2. Lake City DOT Analysis

The Lake City DOT site is located at the Lake City DOT office complex in Lake City, FL. The

majority of the terrestrial path between the Lake City Dot and US-41 sites is populated with 60 ft

trees, shown in green in Figure 4.7. There are some buildings located along the path link, but

their heights are only a fraction of that of the trees and thus can be ignored. The tree line and

building heights do not interfere with the LOS link due to the antenna heights; the first Fresnel

Zone is not breached. The LOS link is displayed in red and the first Fresnel Zone is displayed in

blue. The Path Loss 4.0 print summary, shown in Table 4.2, contains information about the

microwave radio used in this project as well as other site data. The FDOT requires five-nines of

reliability for the STN and based on the given criteria Path Loss 4.0 calculated Lake City DOTs

annual multipath plus rain (%-sec) of 99.99789 and 664.49 in percentage and seconds,

respectively. This does not meet the five-nines FDOT standard, but FDOT ITS engineers statethat eleven minutes of annual downtime is not significant and can be ignored as other routing and

redundancy mechanisms are in place to keep the link active with such a small projected

downtime.

Figure 4.7: Path Loss 4.0 Path Profile for Lake City DOT


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Table 4.2: Path Loss 4.0 Print Summary for Lake City DOT

Lake City US 41Elevation (ft) 159.89 86.09Latitude 30 11 42.00 N 29 59 59.00 N

Longitude 082 39 11.00 W 082 35 54.00 WTrue azimuth () 166.29 346.32Antenna model PA8-65D PA8-65DAntenna height (ft) 186 230Antenna gain (dBi) 42.3 42.3Radome loss (dB) 0.6 0.6TX line type E65 RFS E65 RFSTX line length (ft) 186 230TX line unit loss (dB /100 ft) 1.37 1.37TX line loss (dB) 2.55 3.15Connector loss (dB) 0.2 0.2Circ. branching loss (dB) 1.4 1.5Other TX loss (dB) 0.5RX filter loss (dB) 1.5Frequency (MHz) 6855Polarization HorizontalPath length (mi) 13.84Free space loss (dB) 135.94Atmospheric absorption loss (dB) 0.2Field margin (dB) 1

Net path loss (dB) 64.24 63.24Radio model DVM6 Excell DVM6 ExcellTX power (watts) 0.79 0.79TX power (dBm) 29 29EIRP (dBm) 66.05 65.85RX threshold criteria 46.681 Mbps 46.681 MbpsRX threshold level (dBm) -74 -74.9RX signal (dBm) -35.24 -34.24Thermal fade margin (dB) 38.76 40.66Climatic factor 2C factor 6

Fade occurrence factor (Po) 2.67E-01Average annual temperature ( F) 720.01% rain rate (mm/hr) 98Flat fade margin - rain (dB) 38.76Rain attenuation (dB) 38.76Annual multipath + rain (%-sec) 99.99789 - 664.49


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4.2.3.3. SR-222 Analysis

The SR-222 site is located along Interstate 75 at the Exit 390 interchange, outside the

southbound on ramp in Gainesville, FL. The majority of the terrestrial path between the SR-222

and US-41 sites is populated with 60 ft trees, shown in green in Figure 4.8. There are some

buildings located along the path link, but their heights are only a fraction of that of the trees and

thus can be ignored. The rest of the path link is filled with farmland and is treated as open land

in Path Loss 4.0. The tree line and farmland do not interfere with the LOS link due to the

antenna heights; the first Fresnel Zone is not breached. The LOS link is displayed in red and the

bottom half of the first Fresnel Zone in blue. The Path Loss 4.0 print summary, as shown in

Table 4.3, contains information about the microwave radio used in this project among as well as

site data. The FDOT requires five-nines of reliability for the STN. Based on the given criteria

Path Loss 4.0 calculated SR-222s annual multipath plus rain (%-sec) of 99.98588 and 4453.21in percentage and seconds, respectively. This is below FDOT standards and has been reported to

FDOT ITS engineers.

Figure 4.8: Path Loss 4.0 Path Profile for SR-222


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Table 4.3: Path Loss 4.0 Print Summary for SR-222

SR-222 US 41Elevation (ft) 121.5 86.09Latitude 29 41 15.52 N 29 59 59.00 N

Longitude 082 26 45.85 W 082 35 54.00 WTrue azimuth () 337 156.92Antenna model PA8-65D PA8-65DAntenna height (ft) 221 290Antenna gain (dBi) 42.3 42.3Radome loss (dB) 0.6 0.6TX line type E65 FRS E65 FRSTX line length (ft) 221 290TX line unit loss (dB /100 ft) 1.37 1.37TX line loss (dB) 3.03 3.97Connector loss (dB) 0.2 0.2Circ. branching loss (dB) 1.4 1.5Other TX loss (dB) 0.5RX filter loss (dB) 1.5Frequency (MHz) 6815Polarization HorizontalPath length (mi) 23.36Free space loss (dB) 140.43Atmospheric absorption loss (dB) 0.34Field margin (dB) 1

Net path loss (dB) 65.77 65.77Radio model DVM6 Excell DVM6 ExcellTX power (watts) 0.79 0.79TX power (dBm) 29 29EIRP (dBm) 67.47 66.53RX threshold criteria 46.681 Mbps 46.681 MbpsRX threshold level (dBm) -74.9 -74.9RX signal (dBm) -36.77 -36.77Thermal fade margin (dB) 38.13 38.13Climatic factor 2C factor 6

Fade occurrence factor (Po) 1.27E+00Average annual temperature ( F) 720.01% rain rate (mm/hr) 98Flat fade margin - rain (dB) 38.13Rain attenuation (dB) 38.13Annual multipath + rain (%-sec) 99.98588 - 4453.21


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4. 3. Correlation Analysis without Data Preprocessing

The correlation coefficients of the data for each site were calculated and are shown in Tables 4.4

through 4.7. The correlation coefficients of the RSL and other weather parameters such as wind

speed, relative humidity, temperature, precipitation, etc. for each site are very weak which

indicates that there is not a direct correlation between the RSL and weather parameters, and that

they are independent of each other. This does not hold true in observations and other studies. A

timing delay errors or non-synchronized timing errors may be the cause of the low correlation

values; a result from variations of antenna heights and sensor locations or preprocessing of the

data may be needed.

Table 4.4: Correlation Coefficients for Greenville

RSL WS WSA WD P RH BP T WC HI DP

RSL 1 0.012 0.005 0.031 -0.054 -0.065 0.032 0.001 -0.004 -0.017 -0.068

WS 0.012 1 0.202 -0.005 -0.023 -0.394 0.035 0.242 0.249 0.242 -0.110

WSA 0.005 0.202 1 -0.013 0.042 -0.122 0.088 -0.071 -0.053 -0.052 -0.199WD 0.031 -0.005 -0.013 1 -0.026 0.002 0.161 -0.061 -0.062 -0.083 -0.074

P -0.054 -0.023 0.042 -0.026 1 0.155 -0.170 -0.063 -0.064 -0.088 0.078RH -0.065 -0.394 -0.122 0.002 0.155 1 -0.081 -0.666 -0.659 -0.634 0.238

BP 0.032 0.035 0.088 0.161 -0.170 -0.081 1 -0.077 -0.078 -0.071 -0.172T 0.001 0.242 -0.071 -0.061 -0.063 -0.666 -0.077 1 0.988 0.961 0.548

WC -0.004 0.249 -0.053 -0.062 -0.064 -0.659 -0.078 0.988 1 0.972 0.553

HI -0.017 0.242 -0.052 -0.083 -0.088 -0.634 -0.071 0.961 0.972 1 0.560DP -0.068 -0.110 -0.199 -0.074 0.078 0.238 -0.172 0.548 0.553 0.560 1

Table 4.5: Correlation Coefficients for Lake City DOT


RSL 1 0.005 0.008 0.058 -0.059 -0.086 0.052 0.066 0.079 0.085 -0.015

WS 0.005 1 0.995 0.076 -0.045 -0.286 0.532 0.018 -0.036 0.013 -0.239WSA 0.008 0.995 1 0.077 -0.046 -0.293 0.543 0.018 -0.036 0.014 -0.245

WD 0.058 0.076 0.077 1 0.009 -0.227 0.069 0.191 0.236 0.227 -0.049

P -0.059 -0.045 -0.046 0.009 1 0.186 -0.133 -0.060 -0.084 -0.102 0.102RH -0.086 -0.286 -0.293 -0.227 0.186 1 -0.562 -0.295 -0.482 -0.407 0.648BP 0.052 0.532 0.543 0.069 -0.133 -0.562 1 -0.200 -0.010 -0.006 -0.654

T 0.066 0.018 0.018 0.191 -0.060 -0.295 -0.200 1 0.930 0.857 0.525

WC 0.079 -0.036 -0.036 0.236 -0.084 -0.482 -0.010 0.930 1 0.923 0.307HI 0.085 0.013 0.014 0.227 -0.102 -0.407 -0.006 0.857 0.923 1 0.343

DP -0.015 -0.239 -0.245 -0.049 0.102 0.648 -0.654 0.525 0.307 0.343 1


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Table 4.6: Correlation Coefficients for SR-222


RSL 1 0.099 0.077 -0.052 -0.090 0.045 0.057 0.044 0.065 0.046 0.059

WS 0.099 1 0.580 -0.028 -0.076 0.130 0.146 -0.018 0.024 0.051 0.187WSA 0.077 0.580 1 -0.057 -0.047 -0.150 0.155 -0.138 -0.160 -0.142 -0.153

WD -0.052 -0.028 -0.057 1 0.048 0.043 -0.240 0.028 0.039 0.054 0.047

P -0.090 -0.076 -0.047 0.048 1 -0.091 -0.140 0.001 -0.037 -0.021 -0.097RH 0.045 0.130 -0.150 0.043 -0.091 1 0.263 -0.241 0.107 -0.073 0.958

BP 0.057 0.146 0.155 -0.240 -0.140 0.263 1 -0.085 0.056 -0.005 0.268T 0.044 -0.018 -0.138 0.028 0.001 -0.241 -0.085 1 0.913 0.931 -0.047

WC 0.065 0.024 -0.160 0.039 -0.037 0.107 0.056 0.913 1 0.905 0.272HI 0.046 0.051 -0.142 0.054 -0.021 -0.073 -0.005 0.931 0.905 1 0.143

DP 0.059 0.187 -0.153 0.047 -0.097 0.958 0.268 -0.047 0.272 0.143 1

The correlation coefficient matrix, as shown in Table 4.7, presents little correlation between theselected research locations. This may be due to time-lag or non-synchronized issues and varying

antenna and sensor heights.

Table 4.7: RSL Correlation Coefficients of the Chosen Sites

Greenville Lake City DOT SR-222Greenville 1 0.214 0.089Lake City DOT 0.214 1 0.177

SR-222 0.089 0.177 1

A cross-correlation, the measure of similarity between two waveforms when a time-lag is

applied, is applied to the three sites since the correlation of RSL and weather data appears to be

very small. The output matrices (Tables 4.8, 4.9, and 4.10) of the sample cross-correlation

coefficients are similar to the output matrices for the correlation coefficients (Tables 4.4, 4.5, and

4.6 above). The values of the output matrices must be close to either +1 or -1 to confer a

relationship of dependence. The values of the output matrices for both the correlation coefficient

matrices and sample cross-correlation coefficient matrices are close to zero, thus affirming the

RSL and weather parameters are independent of one another. Preprocessing is needed to find a

correlation between the acquired data.


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Table 4.8: RSL and Weather Parameter Cross-Correlation Coefficients for Greenville

WS WSA WD P RH BP T WC HI DP0.0095 0.0043 0.0279 -0.0486 -0.0537 0.0326 -0.0097 -0.0140 -0.0282 -0.06960.0095 0.0043 0.0278 -0.0486 -0.0542 0.0326 -0.0092 -0.0135 -0.0277 -0.06950.0096 0.0044 0.0277 -0.0484 -0.0548 0.0325 -0.0087 -0.0129 -0.0271 -0.0694

0.0100 0.0043 0.0273 -0.0483 -0.0553 0.0324 -0.0081 -0.0124 -0.0265 -0.06930.0094 0.0044 0.0283 -0.0485 -0.0559 0.0324 -0.0076 -0.0118 -0.0259 -0.06920.0100 0.0045 0.0278 -0.0488 -0.0565 0.0324 -0.0071 -0.0113 -0.0254 -0.06920.0097 0.0046 0.0280 -0.0491 -0.0571 0.0323 -0.0065 -0.0108 -0.0248 -0.06910.0102 0.0047 0.0289 -0.0494 -0.0576 0.0323 -0.0060 -0.0103 -0.0242 -0.06900.0100 0.0049 0.0283 -0.0498 -0.0582 0.0323 -0.0055 -0.0097 -0.0236 -0.06880.0108 0.0051 0.0277 -0.0502 -0.0587 0.0323 -0.0049 -0.0091 -0.0229 -0.06860.0108 0.0053 0.0293 -0.0504 -0.0593 0.0323 -0.0044 -0.0086 -0.0223 -0.06860.0106 0.0054 0.0291 -0.0506 -0.0599 0.0323 -0.0039 -0.0081 -0.0218 -0.06850.0116 0.0055 0.0296 -0.0508 -0.0604 0.0323 -0.0033 -0.0075 -0.0212 -0.06840.0115 0.0056 0.0290 -0.0510 -0.0610 0.0322 -0.0028 -0.0070 -0.0207 -0.06830.0117 0.0056 0.0283 -0.0513 -0.0616 0.0322 -0.0023 -0.0065 -0.0201 -0.0683

0.0116 0.0055 0.0287 -0.0516 -0.0621 0.0322 -0.0018 -0.0060 -0.0196 -0.06820.0116 0.0056 0.0299 -0.0520 -0.0628 0.0322 -0.0013 -0.0055 -0.0191 -0.06830.0117 0.0056 0.0311 -0.0524 -0.0633 0.0322 -0.0008 -0.0050 -0.0186 -0.06820.0121 0.0056 0.0315 -0.0528 -0.0639 0.0322 -0.0003 -0.0045 -0.0181 -0.06820.0119 0.0056 0.0310 -0.0533 -0.0645 0.0322 0.0001 -0.0041 -0.0176 -0.06810.0120 0.0055 0.0308 -0.0538 -0.0650 0.0322 0.0006 -0.0036 -0.0171 -0.06810.0125 0.0054 0.0313 -0.0544 -0.0656 0.0322 0.0010 -0.0032 -0.0166 -0.06800.0119 0.0052 0.0323 -0.0549 -0.0662 0.0322 0.0015 -0.0027 -0.0161 -0.06800.0123 0.0052 0.0323 -0.0555 -0.0667 0.0322 0.0019 -0.0023 -0.0156 -0.06800.0129 0.0053 0.0343 -0.0560 -0.0672 0.0322 0.0024 -0.0019 -0.0152 -0.06800.0127 0.0055 0.0332 -0.0563 -0.0677 0.0322 0.0029 -0.0014 -0.0147 -0.06780.0137 0.0056 0.0337 -0.0567 -0.0682 0.0322 0.0033 -0.0010 -0.0143 -0.0679

0.0139 0.0058 0.0351 -0.0572 -0.0687 0.0322 0.0037 -0.0006 -0.0138 -0.06780.0134 0.0059 0.0359 -0.0576 -0.0691 0.0323 0.0042 -0.0001 -0.0134 -0.06770.0140 0.0059 0.0354 -0.0581 -0.0696 0.0323 0.0046 0.0002 -0.0130 -0.06770.0152 0.0060 0.0361 -0.0586 -0.0700 0.0323 0.0050 0.0006 -0.0126 -0.06760.0146 0.0061 0.0357 -0.0590 -0.0704 0.0324 0.0053 0.0009 -0.0123 -0.06760.0153 0.0062 0.0361 -0.0594 -0.0708 0.0324 0.0057 0.0013 -0.0119 -0.06760.0156 0.0063 0.0356 -0.0598 -0.0713 0.0324 0.0061 0.0016 -0.0117 -0.06770.0157 0.0064 0.0363 -0.0603 -0.0717 0.0324 0.0065 0.0019 -0.0113 -0.06760.0158 0.0064 0.0356 -0.0606 -0.0721 0.0324 0.0068 0.0023 -0.0109 -0.06750.0159 0.0063 0.0358 -0.0611 -0.0725 0.0325 0.0072 0.0026 -0.0106 -0.06750.0164 0.0062 0.0354 -0.0614 -0.0729 0.0324 0.0076 0.0030 -0.0103 -0.06750.0163 0.0061 0.0350 -0.0618 -0.0734 0.0324 0.0079 0.0033 -0.0100 -0.0675

0.0168 0.0060 0.0346 -0.0622 -0.0737 0.0324 0.0083 0.0037 -0.0096 -0.06740.0170 0.0059 0.0348 -0.0625 -0.0741 0.0324 0.0086 0.0040 -0.0093 -0.0674


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Table 4.9: RSL and Weather Parameter Cross-Correlation Coefficients for Lake City DOT

WS WSA WD P RH BP T WC HI DP0.0045 0.0064 0.0622 -0.0496 -0.0795 0.0519 0.0618 0.0753 0.0784 -0.01360.0043 0.0063 0.0622 -0.0500 -0.0797 0.0519 0.0620 0.0756 0.0788 -0.01360.0040 0.0063 0.0624 -0.0503 -0.0800 0.0519 0.0623 0.0759 0.0791 -0.0136

0.0038 0.0063 0.0623 -0.0507 -0.0803 0.0519 0.0625 0.0762 0.0795 -0.01370.0036 0.0063 0.0617 -0.0510 -0.0806 0.0519 0.0628 0.0765 0.0799 -0.01370.0034 0.0063 0.0619 -0.0514 -0.0809 0.0519 0.0630 0.0768 0.0802 -0.01370.0033 0.0064 0.0612 -0.0517 -0.0813 0.0519 0.0632 0.0770 0.0806 -0.01380.0033 0.0065 0.0614 -0.0521 -0.0815 0.0519 0.0634 0.0771 0.0809 -0.01380.0033 0.0067 0.0610 -0.0525 -0.0819 0.0520 0.0636 0.0774 0.0812 -0.01390.0035 0.0069 0.0606 -0.0530 -0.0822 0.0520 0.0639 0.0776 0.0816 -0.01390.0037 0.0071 0.0600 -0.0535 -0.0825 0.0521 0.0640 0.0778 0.0819 -0.01400.0038 0.0073 0.0602 -0.0539 -0.0828 0.0521 0.0642 0.0779 0.0822 -0.01400.0040 0.0075 0.0593 -0.0544 -0.0831 0.0521 0.0644 0.0781 0.0825 -0.01410.0042 0.0077 0.0597 -0.0549 -0.0834 0.0521 0.0645 0.0782 0.0827 -0.01430.0043 0.0079 0.0579 -0.0553 -0.0837 0.0521 0.0647 0.0783 0.0830 -0.0144

0.0045 0.0081 0.0582 -0.0558 -0.0841 0.0521 0.0649 0.0785 0.0834 -0.01450.0047 0.0082 0.0583 -0.0562 -0.0844 0.0522 0.0651 0.0787 0.0838 -0.01450.0048 0.0083 0.0584 -0.0567 -0.0847 0.0523 0.0653 0.0789 0.0840 -0.01460.0048 0.0083 0.0579 -0.0573 -0.0849 0.0523 0.0654 0.0791 0.0843 -0.01470.0047 0.0082 0.0582 -0.0579 -0.0852 0.0523 0.0656 0.0792 0.0846 -0.01470.0046 0.0081 0.0580 -0.0585 -0.0856 0.0523 0.0657 0.0794 0.0848 -0.01490.0046 0.0081 0.0581 -0.0592 -0.0858 0.0522 0.0658 0.0795 0.0850 -0.01490.0047 0.0082 0.0579 -0.0598 -0.0860 0.0522 0.0659 0.0796 0.0852 -0.01500.0048 0.0084 0.0580 -0.0604 -0.0862 0.0522 0.0659 0.0797 0.0853 -0.01510.0050 0.0086 0.0585 -0.0609 -0.0864 0.0523 0.0660 0.0797 0.0855 -0.01520.0052 0.0088 0.0586 -0.0614 -0.0866 0.0524 0.0661 0.0798 0.0856 -0.01530.0054 0.0090 0.0595 -0.0620 -0.0868 0.0524 0.0661 0.0799 0.0857 -0.0154

0.0054 0.0091 0.0595 -0.0625 -0.0870 0.0525 0.0661 0.0799 0.0857 -0.01550.0054 0.0091 0.0593 -0.0629 -0.0872 0.0525 0.0661 0.0800 0.0858 -0.01560.0054 0.0090 0.0586 -0.0633 -0.0873 0.0525 0.0661 0.0800 0.0860 -0.01570.0054 0.0089 0.0587 -0.0636 -0.0875 0.0525 0.0662 0.0801 0.0860 -0.01580.0054 0.0089 0.0588 -0.0641 -0.0876 0.0526 0.0661 0.0801 0.0861 -0.01590.0055 0.0089 0.0591 -0.0645 -0.0877 0.0525 0.0661 0.0801 0.0862 -0.01600.0055 0.0089 0.0589 -0.0648 -0.0879 0.0525 0.0661 0.0801 0.0863 -0.01610.0055 0.0090 0.0582 -0.0652 -0.0880 0.0526 0.0661 0.0801 0.0864 -0.01620.0055 0.0091 0.0584 -0.0657 -0.0881 0.0526 0.0660 0.0801 0.0865 -0.01630.0054 0.0092 0.0593 -0.0660 -0.0882 0.0527 0.0660 0.0801 0.0865 -0.01630.0055 0.0093 0.0588 -0.0664 -0.0883 0.0527 0.0660 0.0802 0.0866 -0.01640.0056 0.0095 0.0587 -0.0666 -0.0884 0.0527 0.0660 0.0802 0.0867 -0.0165

0.0057 0.0096 0.0590 -0.0670 -0.0884 0.0526 0.0659 0.0801 0.0867 -0.01650.0058 0.0098 0.0591 -0.0673 -0.0885 0.0526 0.0659 0.0801 0.0867 -0.0166


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Table 4.10: RSL and Weather Parameter Cross-Correlation Coefficients for SR-222

WS WSA WD P RH BP T WC HI DP0.0998 0.0756 -0.0593 -0.0833 0.0454 0.0597 0.0364 0.0558 0.0382 0.05820.0999 0.0757 -0.0591 -0.0835 0.0454 0.0596 0.0368 0.0563 0.0386 0.05830.0997 0.0758 -0.0588 -0.0839 0.0453 0.0594 0.0372 0.0567 0.0390 0.0583

0.0999 0.0759 -0.0586 -0.0842 0.0453 0.0593 0.0376 0.0571 0.0394 0.05840.0999 0.0759 -0.0589 -0.0847 0.0452 0.0591 0.0380 0.0575 0.0398 0.05850.0999 0.0760 -0.0587 -0.0851 0.0452 0.0590 0.0384 0.0580 0.0402 0.05860.1000 0.0761 -0.0584 -0.0856 0.0452 0.0588 0.0388 0.0584 0.0406 0.05860.0995 0.0761 -0.0580 -0.0860 0.0452 0.0586 0.0392 0.0588 0.0410 0.05870.0994 0.0761 -0.0582 -0.0864 0.0452 0.0585 0.0396 0.0593 0.0414 0.05880.0996 0.0762 -0.0578 -0.0867 0.0452 0.0584 0.0401 0.0597 0.0419 0.05890.0995 0.0763 -0.0560 -0.0870 0.0452 0.0582 0.0404 0.0601 0.0423 0.05890.0993 0.0764 -0.0551 -0.0873 0.0452 0.0580 0.0408 0.0606 0.0427 0.05900.0994 0.0765 -0.0544 -0.0877 0.0452 0.0579 0.0412 0.0610 0.0431 0.05910.0995 0.0765 -0.0551 -0.0879 0.0452 0.0577 0.0417 0.0615 0.0435 0.05920.0995 0.0766 -0.0551 -0.0882 0.0451 0.0576 0.0421 0.0619 0.0439 0.0592

0.0994 0.0767 -0.0553 -0.0884 0.0451 0.0574 0.0425 0.0624 0.0443 0.05920.0993 0.0768 -0.0556 -0.0887 0.0451 0.0573 0.0429 0.0629 0.0448 0.05930.0992 0.0768 -0.0549 -0.0889 0.0451 0.0571 0.0433 0.0633 0.0452 0.05940.0992 0.0768 -0.0533 -0.0892 0.0451 0.0570 0.0437 0.0638 0.0456 0.05940.0991 0.0768 -0.0528 -0.0894 0.0450 0.0568 0.0441 0.0642 0.0460 0.05940.0993 0.0768 -0.0519 -0.0895 0.0450 0.0567 0.0445 0.0646 0.0463 0.05940.0991 0.0769 -0.0512 -0.0897 0.0450 0.0566 0.0449 0.0650 0.0467 0.05950.0992 0.0769 -0.0506 -0.0901 0.0450 0.0565 0.0452 0.0654 0.0470 0.05950.0992 0.0770 -0.0502 -0.0904 0.0449 0.0564 0.0456 0.0658 0.0474 0.05950.0992 0.0771 -0.0505 -0.0906 0.0449 0.0562 0.0460 0.0662 0.0477 0.05960.0992 0.0771 -0.0509 -0.0909 0.0449 0.0560 0.0463 0.0665 0.0481 0.05960.0993 0.0771 -0.0503 -0.0911 0.0449 0.0559 0.0466 0.0669 0.0485 0.0598

0.0996 0.0772 -0.0503 -0.0913 0.0449 0.0557 0.0470 0.0673 0.0488 0.05980.0999 0.0772 -0.0503 -0.0915 0.0450 0.0556 0.0473 0.0677 0.0491 0.05980.1000 0.0772 -0.0501 -0.0917 0.0450 0.0554 0.0477 0.0681 0.0494 0.06000.0998 0.0771 -0.0510 -0.0919 0.0450 0.0553 0.0480 0.0685 0.0497 0.06010.0997 0.0770 -0.0505 -0.0922 0.0452 0.0552 0.0483 0.0689 0.0500 0.06030.0993 0.0770 -0.0500 -0.0926 0.0452 0.0550 0.0486 0.0693 0.0503 0.06040.0990 0.0770 -0.0492 -0.0928 0.0452 0.0549 0.0489 0.0696 0.0506 0.06050.0990 0.0769 -0.0483 -0.0930 0.0453 0.0548 0.0492 0.0700 0.0508 0.06050.0989 0.0769 -0.0484 -0.0932 0.0453 0.0546 0.0495 0.0703 0.0511 0.06080.0987 0.0769 -0.0480 -0.0932 0.0454 0.0545 0.0497 0.0706 0.0513 0.06090.0985 0.0770 -0.0479 -0.0933 0.0454 0.0544 0.0500 0.0709 0.0515 0.06090.0982 0.0770 -0.0481 -0.0934 0.0455 0.0543 0.0502 0.0712 0.0518 0.0611

0.0984 0.0770 -0.0483 -0.0935 0.0455 0.0541 0.0505 0.0715 0.0520 0.06120.0987 0.0770 -0.0484 -0.0937 0.0455 0.0540 0.0507 0.0718 0.0522 0.0613


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4.4. Fast Fourier Transform and Power Spectrum Analysis

The Discrete Fourier Transform (DFT) decomposes a sequence of values in a function from their

time domain representation to their frequency domain representation. The Fast Fourier

Transform (FFT) is a faster variation of the DFT algorithm and is able to compute the DFT and

its inverse. The FFT requires only log individual steps and transforming is worthwhile

when log , where L is the vector length [12]. The FFT is defined as 0,, 1 (4.1)

and the multidimensional FFT is defined as

(4.2)4.4.1. Fast Fourier Transform AnalysisThe multidimensional FFT was used to compute data in MATLAB R2007b and a sample of this

computation is presented in Figure 4.9.

Figure 4.9: FFT of Greenville RSL and ESS Data


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The FFT is not recommended to analyze non-stationary signals since it cannot distinguish the

two or multiple signals very well. The FFT sees both signals as the same and constituted of the

same frequency components, as shown in Figures 4.9 and 4.10. Thus the FFT is not a suitable

tool for analyzing non-stationary signals or time-varying spectra. This information was found

after analysis was well under way and the rest of section 4.4 displays evidence for this argument.

Figure 4.10: Enlarged Window of the FFT of Greenville RSL and ESS Data

4.4.2. FFT Power Spectrum Analysis

The power spectrum of the FFT is very noisy and it is difficult to infer any correlation. Figures

4.11 and 4.12 present the power spectrum for Greenville over one day and one hour period,

respectively. From these figures it is clear that the power spectrum is not only distorted but also

a low method for determining any true correlation.


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Figure 4.11: Power Spectrum of Greenville RSL and ESS data for One Day

Figure 4.12: Power Spectrum of Greenville RSL and ESS data for a One Hour


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4.4.3. Correlation Analysis

The correlation analysis shows very high correlation between RSL and all weather parameters,

but this is only a strong correlation between the frequency components, not the spatial

correlation. See Table 4.11 below.

Table 4.11: FFT Correlation Coefficients for Greenville

RSL WS WSA WD P RH BP T WC HI DPRSL 1 0.923 0.986 0.952 0.875 0.993 0.993 0.875 0.952 0.986 0.923WS 0.923 1 0.968 0.980 0.980 0.958 0.958 0.984 0.981 0.966 0.998WSA 0.986 0.968 1 0.984 0.934 0.997 0.997 0.939 0.986 0.998 0.966WD 0.952 0.980 0.984 1 0.977 0.979 0.978 0.972 0.997 0.986 0.981P 0.875 0.980 0.934 0.977 1 0.922 0.922 0.987 0.972 0.939 0.984RH 0.993 0.958 0.997 0.979 0.922 1 1.000 0.922 0.978 0.997 0.958BP 0.993 0.958 0.997 0.978 0.922 1.000 1 0.922 0.979 0.997 0.958T 0.875 0.984 0.939 0.972 0.987 0.922 0.922 1 0.977 0.934 0.980WC 0.952 0.981 0.986 0.997 0.972 0.978 0.979 0.977 1 0.984 0.980HI 0.986 0.966 0.998 0.986 0.939 0.997 0.997 0.934 0.984 1 0.968DP 0.923 0.998 0.966 0.981 0.984 0.958 0.958 0.980 0.980 0.968 1

4.5. Short Time Fourier Transform and Power Spectrum Analysis

The Short Time Fourier Transform (STFT) is a Fourier related transform that is used to

determine the sinusoidal frequency and phase content of local sections of a signal as it changes

over time. This method is accurate only for a specific time and frequency resolution.

Heisenbergs uncertainty principle states the momentum and position of a moving particle cannot

be known simultaneously. This can be applied to signals and other discrete data. In the case of

frequency and time, the spectral component cannot be known at a given instant. This may cause

noise in the result of the STFT, either in the frequency or time resolutions. The power spectrum

is a function of frequency and is a deterministic function of time. It has dimensions of power per

Hz or energy per Hz and helps to identify periodicities, and is utilized to correlate RSL and

various weather conditions.

4.5.1. Short Time Fourier Transform Analysis

The STFT breaks the data to be transformed into block sections or windows along the signal

under analysis and performs the FT within the windows. The complex result is added to a


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matrix, which records magnitude and phase for each point in time and frequency. The STFT can

be expressed as

(4.3)The exponent determines the resolution of the frequency component in the STFT. When the

window or frame is small the time resolution is high, but the frequency resolution is low due to

the Heisenbergs uncertainty principle.

4.5.2. STFT Power Spectrum Analysis

The power spectrum of the STFT was computed for a small portion of data from the Greenville

ESS site. A 3-D plot of the STFT, time vs. frequency vs. power, is shown in Figure 4.13. The

frequency component resolution is very well defined and has distinguishable amplitude or

power, as shown in Figure 4.14, but the time resolution is low. The time-axis is very noisy or

distorted. Figure 4.15 shows amplitude vs. time. The time values are very long and blend

together, thus a lot of noise or distortion is clearly present in the signal.

Figure 4.13: RSL STFT at 45 Angle for Greenville ESS Rotated Approximately 180


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Figure 4.14: RSL STFT Frequency vs. Power for Greenville ESS

Figure 4.15: RSL STFT Time vs. Power for Greenville ESS


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The correlation analysis is not computed for the STFT due to the fact that the STFT did not yield

clear results. In the FFT the kernel window ranges from - to + . The STFT has

windows of finite length, covering only a small portion of the signal, which in turn reduces the

frequency resolution [18]. The location of the exact frequency components that exist in the

signal is no longer known, only the band of frequencies that exist are known. An example of this

is the FFT example in section 4.4.1. The dilemma occurs in the choice of window size. When

the window is increased, the frequency resolution increase (and time resolution decreases) and

when the window is decreased the frequency resolution decreases (and time resolution

increases).

4.6. Discrete Wavelet Transform and Wavelet Decomposition Analysis

The Discrete Wavelet Transform (DWT) in MATLAB performs a single-level 1-D wavelet

decomposition with respect to a particular wavelet. The wavelet name chosen for this project is

Daubechies. In general the Daubechies wavelets are chosen to have the highest number A of

vanishing moments, (yet this does not imply the best smoothness) for given support width N=2A ,

and among the 2 A 1 possible solutions the one is chosen whose scaling filter has extremal phase

[12]. The DWT provides sufficient information both for analysis and synthesis of the original

signal and with a reduction in computation time. One level of decomposition and canmathematically be expressed as follows:

2 (4.4) 2 (4.5)where y high[k] and y low[k] are the outputs of the highpass and lowpass filters, respectively, after

subsampling by 2 [18].

4.6.1. Wavelet Decomposition Analysis

The DWT (single-level wavelet decomposition) analyzes signals at different frequency bands at

different resolutions: coarse approximation and detailed information. The DWT incorporates

two sets of functions scaling functions (associated with lowpass filters) and wavelet functions

(associated with highpass filters). The decomposition of a sampled signal into different


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original signal will appear as high amplitudes in the region of the DWT signal that include those

particular frequencies. Unlike the FFT, the DWT will not lose time localization of frequencies.

2 (4.6) 2 2

(4.7)

In Figure 4.17 the stages of a three level wavelet decomposition are presented

Figure 4.17: Stages of a Three Level Wavelet Decomposition

More than three levels could have been applied and as more levels are applied to the

wavelet decomposition, more of the input signal is filtered. This can theoretically dampen the

signal too much and the results would then appear as zero or near zero amplitude. Three levels

of decomposition are necessary to view the similarities between the RSL and weather

parameters. The three research sites for this project displayed a correlation between RSL at each

site location and their respected weather conditions after a three level wavelet decomposition

was calculated. Figure 4.18 - Figure 4.24 present various wavelet decomposition trials at various

scales. The precipitation parameter shows little correlation or temporal symmetry to the RSL.

This observation holds true for each site. The results for Greenville are shown in Figure 4.18.

The RSL and precipitation for Lake City DOT, as shown in Figure 4.21, has a smaller window

and the results more apparent.


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Figure 4.18: Wavelet Decomposition of Precipitation and RSL for Greenville Data

Observations of the original data, with no preprocessing, presented a correlation between

the temperature, relative humidity, and received signal level. Attenuation is present during

increasing humidity and decreasing temperature with no presence of wind. It is normal to have adecrease in signal strength during early morning hours and many observations made by FDOT

employees have confirmed this. The RSL, RH, and T wavelet decompositions for Greenville,

Lake City DOT, and SR-222 are shown in Figures 4.20, 4.22, 4.24, respectively. The three level

wavelet decomposition removed noise and distortion from the signal and presented the scaled

frequency components in the time domain allowing the attenuation and gain characteristics

viewable for analysis. Reviewing the data and wavelet analysis has shown that the major factors

in attenuation are wind speed, relative humidity, and temperature. When the temperature

decreases and the relative humidity increases, the presence of high water vapor or fog occurs.

Studying of the data displays more attenuation when wind is not present. This leads to still or

slowly rising water vapor or fog and at the 6.8 GHz frequency these atmospheric conditions

cause visible attenuation in the signal. More on this will be discussed in Chapter 5.


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Figure 4.19: Wavelet Decomposition for RSL, RH, and T at Greenville ESS Site

Figure 4.20: Enlarged Wavelet Decomposition for Greenville Data


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Figure 4.21: Wavelet Decomposition of Precipitation and RSL for Lake City DOT Data

Figure 4.22: Enlarged Wavelet Decomposition for Lake City DOT Data


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Figure 4.23: Wavelet Decomposition of Precipitation and RSL for SR-222 Data

Figure 4.24: Enlarged Wavelet Decomposition for SR-222 Data


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A three level wavelet decomposition of the data removed noise and distortion from the data.

Most correlation coefficients for all sites show a strong spatial correlation between

Study of Correlations Between Microwave Transmissions and Atmosph

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